摘要:

AbstractA numerical approximation is taken to the solution of the complex flows existing in gas turbine engines with transonic blading. The quasi‐3D approach decouples the problem into through‐flow and blade‐to‐blade solutions. An industrially practical finite element through‐flow solution is developed and for blade‐to‐blade solutions a transonic finite areas method is utilized. The finite element code developed is capable of operating in an analysis or a design mode. In both modes a dynamic relaxation factor is employed and considerable reduction in solution time can be achieved. Comparisons to streamline curvature methods are carried out for simple analytical and complex indust

ISSN:0271-2091    

DOI:10.1002/fld.1650030103

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractA variational formulation for the solution of two dimensional, incompressible viscous flows has been developed by one of the authors.1The main objective of the present paper is to demonstrate the applicability of this approach for the solution of practical problems and in particular to investigate the introduction of boundary conditions to the Navier‐Stokes equations through a variational formulation. The application of boundary conditions for typical internal and external flow problems is presented. Sample cases include flow around a cylinder and flow through a stepped channel.Quadrilateral, bilinear isoparametric elements are utilized in the formulation. A single‐step, implicit, and fully coupled numerical integration scheme based on the variational principle is employed. Presented results include sample cases with different Reynolds numbers for laminar and turbulent flows. Turbulence is modelled using a simple mixing length model. Numerical results show good agreement with existing soluti

ISSN:0271-2091    

DOI:10.1002/fld.1650030104

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractThe three dimensional linear hydrodynamic equations which describe wind induced flow in a sea are solved using the Galerkin method. A basis set of eigenfunctions is used in the calculation. These eigenfunctions are determined numerically using an expansion of B‐splines.Using the Galerkin method the problem of wind induced flow in a rectangular basin is examined in detail. A no‐slip bottom boundary condition with a vertically varying eddy viscosity distribution is employed in the calculation. With a low (of order 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s near the sea bed together with high current shear in this region are physically realistic and have been observed in the sea.In order to accurately compute the eigenfunctions associated with large (of order 2000 cm2/s at the sea surface to 1 cm2/s at the sea bed) vertical variation of viscosity, an expansion of the order of thirty‐five B‐splines has to be used. The spline functions are distributed through the vertical so as to give the maximum resolution in the high shear region near the sea bed.Calculations show that in the case of a no‐slip bottom boundary condition, with an associated region of high current shear near the sea bed, the Galerkin method with a basis set of the order of ten eigenfunctions (a Galerkin‐eigenfunction method) yields an accurate solution of the hydrodynamic equations. However, solving the same problem using the Galerkin method with a basis set of B‐splines, requires an expansion of the order of thirty‐five spline functions in order to obtain the same accuracy.Comparisons of current profiles and time series of sea surface elevation computed using a model with a slip bottom boundary condition and a model with a no‐slip boundary condition have been made. These comparisions show that consistent solutions are obtained from the two models when a physically relistic coefficient of bottom friction is used in the slip model, and a physically realistic bottom roughness length and thickness of the bottom boundary layer are employed in

ISSN:0271-2091    

DOI:10.1002/fld.1650030105

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractFrom the linearized, time‐independent, constant depth, shallow water tidal equations in anf‐plane for a two‐layer estuary, two independent modal Helmholtz equations are derived. These modal equations are solved using a fifth‐degree finite element technique. The first and second space derivatives of the complex modal tidal elevations, and thus the modal currents and their first derivatives, are evaluated directly from the solution at each node of the finite element mesh.The Stokes drift, which is the major part of the residual tidal flow, is evaluated from these nodal values of the currents and their derivatives. Good agreement is obtained with the exact analytical solution for a wedge‐shaped estuary with a wedge angle of π/3, using a mesh of 64 equilateral triangles with sides approximately 1/10 of the wavelength 2πC2/σ of a Kelvin wave solution for the short‐w

ISSN:0271-2091    

DOI:10.1002/fld.1650030106

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractA formulation of the boundary element method for the solution of non‐zero Reynolds number incompressible flows in which the non‐linear terms are lumped together to form a forcing function is presented. Solutions can be obtained at low to moderate Reynolds numbers. The method was tested using the flow of a fluid in a two‐dimensional converging channel (Hamel flow) for which an exact solution is available. An axisymmetric formulation is demonstrated by examining the drag experienced by a sphere held stationary in uniform flow. Performance of the method was satisfactory. New results for an axisymmetric free jet at zero Reynolds number obtained using the boundary element method are also included. The method is ideal for this type of free‐surface

ISSN:0271-2091    

DOI:10.1002/fld.1650030107

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650030108

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650030109

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650030102

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY